The Polymerization of Ethylene under High Pressure using the Semiconductor Model
Zeljko
Prebeg, Lermanova 12a, 10000 Zagreb, Croatia
Abstract: By examining the process of heat transfer at tubular reactor for LD-PE synthesis, it can be concluded that free electrons exists during polymerization. Additionally, no free electrons occur in the absence of polymerization. A model that can explain and describe this behavior of ethylene under high pressure is the semiconductor model.
Keywords: high-pressure,
polymerization, ethylene, semiconductor, Pauli exclusion principle, molecular
interaction.
Methods:
For examination of physical and chemical states of ethylene under syntheses condition, heat transfer in a reactor for LD-PE synthesis is used. Polymerization of ethylene is highly exothermic reaction. The heat of polymerization ( 94.5 kJ mol-1 ) is continually removed by conduction trough reaction medium or by convection through the reactor's wall. In a high-pressure tubular reactor, about 50% heat of polymerization is carried out through the reactor's wall. The resistance to heat transfer is significant. Common opinion1 is that polymer's deposit isolates the wall of the reactor.
Figure 1. Reactor for LD-PE synthesis.
The shape of the reactor is tubular where 50% of fresh ethylene is injected at several places down reactor’s length (figure 1). The reactor is divided into several heating and cooling zones. The first zone is used for the heating of ethylene to the reaction temperature and while in other zones where the reactions take place, heat is being removed. To calculate the heat transfer coefficient, the temperature and flow of cooling water along with the temperature within the reaction medium are continually measured as shown in figure 2 below.
Figure 2. Measuring of temperature, cooling water flow and temperature of reaction's medium in tubular reactor for LD-PE synthesis.
Flow is measured with the orifice, while temperatures are measured by a thermocouple. During the measuring of temperatures in reactor, high fluctuations have occurred ( +/- 0.5 - 5.0 0C). These fluctuations are proper and are caused by dissipation of the high local energy from the heat of polymerization. In absence of polymerization, these fluctuations do not exist. Heat transferred into the cooling water per unit of time is calculated by following equation:
Q = G*Cp*(tin
– tout)
Where: Q (kJ s-1) is heat transferred into the cooling water
G (kg s-1) is the water flow
Cp is specific heat capacity of water at constant pressure (4.19 kJ/kg/K)
t (K) is the temperature of cooling water.
The transitivity of heat through the wall of the reactor is calculated by equation:
K*A = Q/Dtavg
Where: K (kW m-2 K-1) is the heat transfer coefficient
A (m2) is the surface area for the transfer of heat
Dtavg (K) is average logarithm's difference of temperature
K*A (kW K-1) is the transitivity of heat2 through the wall of reactor.
The average log (temperature) is calculated by the equation, Dtavg = (Dt1-D t2) / log(Dt1/Dt2), with the terms for Dt1 and Dt2 being shown in figure 3 below.
Figure 3. Dt1, Dt2 for a) countercurrent, b) concurrent heat exchanger.
Table 1. Flow, input, and output temperature of cooling water and transferred heat in reactor for LD-PE synthesis.
Table 2. Transitivity of heat trough the wall of reactor
Figure 4. Transitivity of heat through the wall of the reactor (according table 2).
Discussion:
Table 2 and moreover figure 4, show the transitivity of heat through the wall of the reactor. The behavior of second zone is unusual. Heat, liberated by polymerization reaction, heat reaction of the medium itself. None of heat is transferred through the wall of reactor. Other zones show a large resistance for heat transfer through the wall, but this resistance decreases along the reactor. If the polymer film isolates within the reactor, then according to common interpretation, the largest concentration of polymer would be on the end of reactor causing the largest resistance. In reality it is the opposite. Along the end of reactor, resistance to heat transfer through the wall of reactor decreases ( figure 4, table 2 ). It especially occurred in ALD zone where concentration of polymer is greatest, while the transitivity of heat is same as in first zone. From this observation it can be concluded that the polymer does not represent resistance in the heat transfer during polymerization. Similar results are presented by Molen3 in the investigation of two different configurations of heater-reactor system (figure 5). In a TT configuration, heat transfer and conversion in the second reactor is lower than in the first reactor. In a VT configuration, conversion in the tubular reactor is not under significant influence from polymer that is formed in the vessel reactor. In other words, if through the second reactor passes the same quantity of polymer formed at the vessel or tubular heater, the heat transfer trough the wall of the reactor is higher in the VT configuration. This fact shows that the deposit of polymers is not the cause of heat transfer resistance through the wall of the tubular reactor.
Figure 5. Configuration of heater-reactor system. (a) TT (b) VT
Figure 6. Shows the ratio of heat transferred through the wall of reactor and autothermics heat. At conversion of 13 % at first reactor, second reactor ( configuration TT ) works adiabatic. (Hw/Ha=0). At same conversion of 13%, configuration VT shows heat transfer through the wall of reactor (Hw/Ha=1/2). This fact shows that deposit of polymers are not cause of autothermic heat transfer.
But, if the heat transfer is examined as transfer of heat
by the lowest resistance, then it can next be concluded that during the
polymerization, heat is transferred through
the reaction
medium (conduction ) better
then through
the reactor's
wall ( convection ).
In the
absence of polymerization,
the reaction medium shows resistance. Heat
is transferred through the reactor's wall.
It is well known that free electrons cause conduction's heat transfer and
since heat can be transferred by conduction, it can therefore be
concluded that during the
polymerization, free electrons exist. The
model which describes this behavior of matter, is known, and it is used for the
interpretation of semiconductor properties.
Before deduction of the semiconductor
model, the chemical bond will be discussed.
The chemical bond is formed between two atoms by valence electrons. Three kinds of chemical bonds are known. Covalent bonds are formed between atoms of similar electronegativity (figure 7a) where each atom gives one electron to form the bond. An ionic bond has formed between atoms of different electronegativity (figure 7b). In this case, the bonding orbit has moved in the direction of the electronegative atom. The ionic bond can be viewed as a special case of the covalent bond. The third kind of chemical bond is the metallic bond ( figure 7c ). It is formed between a group of atoms where common orbits are connected and form a common band. It will be showed that the metallic bond is a kind of super-bonding of the covalent or ionic bond and strongly depends on the state of the matter.
The ethylene molecule has six chemical bonds. Four of the bonds are formed between carbon and hydrogen (E=411 kJ/mol). Two other bonds are formed between the carbon atoms (Esigma=335 kJ/mol, Epi=607 kJ/mol as shown in figure 8 below).
Valence electrons of molecule of ethylene are electrons on highest energy level. They are forming outer sphere for interaction (figure 9 below).
Figure 9. Interaction
According to the presented knowledge about behavior of
ethylene under
synthesis conditions and on
the base of the semiconductor theory, the following model of
organization for ethylene is proposed.
The deduction of
the semiconductor
model is based
upon an
organized system called a
bimolecule.
Figure 10. Bimolecule forming (Pauli exclusion principle).
The bimolecule of ethylene is formed between two molecules by the excitation of the pi-bound electrons (figure 10). Common orbits are formed at the highest energy levels, while other pi-bound electrons stay unpaired. This transformation, results from the transfer of the pi-bound electrons from the base to excited state using the energy obtained through compression. Proposal for the existence of bimolecule is not a new. Even Pease4 in 1931, during investigation of thermally initiated polymerization at low pressure, proposed that the step before the chemical reaction is the formation of a dimmer of ethylene. On the basis of experimental measurements of the energy of activation and order of reaction, Buback5 concludes that through the thermally initiated polymerization, a biradical dimmer is formed. This authors did not examine the dimmer as a stable form. Stoiljkovic6, had the opinion that bimolecule is a stable particle and that is base of the organization of ethylene. This model is similar to his interpretation of the bimolecule, while the semiconductor model examines energetic transformation.
Figure 11. Valence
band formation.
In an organized system, the valence band is forming by a
partial crossing of
outer orbits of bimolecules
(figure 11). Electrons are
dislocated, but they are still bonded to the bimolecule.
This bond is then weakly bonded in the isolated bimolecule.
The analogy to the semiconductor model proposes that
forbidden zone also exists. The
energy of this forbidden zone is higher than the valence band but lower
than that of the conduction band ( as shown in
figure 12 ). In
addition, a subvalence zone
exists too. The subvalence
zone is formed by unpaired
electrons. It is via these definitions that the semiconductor model of ethylene
is defined (as illustrated in figure 12).
Figure 12. The semiconductor model of ethylene organization.
The semiconductor
model differs
from Stoiljkovic’s
model, which
proposes existent
of oligomolecules in Sr<1 (gamma-phase) and bimolecules in Sr>1
(beta-phase). According
to the semiconductor model, the beta-phase is ordered by the probable
transfer of electrons from valence band to the conduction band.
The initiation of polymerization can occur in different ways ( thermally, chemically, by gamma ray, UV). Understanding the thermal activation of polymerization helps in understanding the analogy between the behavior of an ideal semiconductor and that of ethylene under high pressure. For instance, it is well known that in lower temperatures, the ideal semiconductor behaves as an isolator, (i.e. free electrons do not exist). Increasing of the temperature, some electrons from the valence band get enough energy to transfer from the valence band to conduction band. In the valence band, a hole is formed while the free electron being dislocated in the conduction band.
Figure
13. The initiation of polymerization.
After the excitation of the
electron in the conduction band ( figure 13a ), an unpaired electron
from the valence zone can stay in the valence
zone (figure 13b) or it can be transferred
to the subvalence level (because
holes exist in subvalence level).. In the latter
case an electron - hole cup is formed.
The electron
is dislocated
at conduction
band, while a
hole is relocated at
subvalence zone. This pair plays a
specific role in the chemical reaction and may be
described as a primary radical - terminator pair.
Primary radical plays
a role in starting
polymer chain growth, while terminator plays a role at the
end of the polymer chain growth. These cups are
connected with beta-phase while cups are not formed in the
gamma-phase. There istherefore a significant difference
between the radical and terminator. While the radical is being dislocated (being put
in motion), the terminator is being located, (becoming motionless).
According to the classical explanation, polymer growth is occurring by chain reaction. The heat of polymerization is high, and once it polymerizes 2-3 molecules of ethylene, the breaking of the C-C bound is possible. If efficiently heat transfer does not exist then the formed polymer will be of low molecular weight. It can be shown7 that for a 50% probability of getting a polymer chain of 1000 monomer units, probability for each step of polymer growth must be higher then 1400/1. This shows that an efficient mechanism for stabilization of a radical must exist. The growing of a polymer chain occurs by the filling of holes in the subvalence zone. After the first hole of bimolecule (figure 14a) is filled, a common electron cup has unformed. One electron fills each particular bimolecule, (figure 14b) while the other is free to transfer to hole of nearest bimolecule (figure 14 b, c).
The bimolecule is polymerized in the basic growth reaction.
The electrons are transferred from the highest to the lowest energy state,
causing the liberation
of energy.
Polymerization is
an exothermic reaction. Unpaired
electrons in
valence band
are partially
dislocated, but
still connected to a particular bimolecule. It can therefore
be reasoned
that an
external force
is necessary for this movement
to occur.
Growing a
polymer chain is a
diffusion - controlled reaction, and the radical is stable, while being
partially dislocated at the valence band.
According to classical model, a reaction of end chain
growth is made by the interaction
of two radicals. This
reaction is connected to the free hole in the subvalence level (i.e.
terminator). The free electron from
valence band fills the free holes
in subvalence zone
and the
polymer chain growth is then
finished. (figure 15). If a
terminator does not exist then the growth of the polymer chains will continue
and the polymer chain will have high molecular weight.
Figure 15. End of chain growing
Conclusion:
The heat transfer by convection in absence of polymerization and heat transfer by conduction through the reaction medium during polymerization shows that free electrons exist during the polymerization of ethylene under high pressure. These facts indicate that ethylene under high pressure is semiconductor. Existence of a valence and conduction zone makes possible efficient transfer of the heat of polymerization, without the breaking of the polymer chain. The long life of radicals shows that a mechanism for his stabilization exists and one way is the dislocation of free electrons in the valence or conduction band. During the initiation of polymerization, a primary radical - terminator pair is formed. Primary radical plays a role in starting polymer chain growth, while terminator plays a role at the end of the polymer chain growth. If a terminator does not exist then the growth of the polymer chains will continue and the polymer chain will have high molecular weight. Future direct measurement of the electrical properties would be the best way to proving this semiconductor model of ethylene polymerization.
References:
I wish to acknowledge Prof. Mitsuo Sawamoto for his useful suggestions in the preparation of this manuscript. Also, many thanks to Victoria at the Journal of Theoretics.